Set constraint model and automated encoding into SAT: application to the social golfer problem

Abstract

On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively model set constraint problems and to encode them automatically into SAT instances. We apply our technique to the Social Golfer Problem and we also use it to break symmetries of the problem.Our technique is simpler, more declarative, and less error-prone than direct and improved hand modeling. The SAT instances that we automatically generate contain less clauses than improved hand-written instances such as in [20], and with unit propagation they also contain less variables. Moreover, they are well-suited for SAT solvers and they are solved faster as shown when solving difficult instances of the Social Golfer Problem.

Solving complex problems using model transformations: from set constraint modeling to SAT instance solving

“…Moreover, it is expressive and very intuitive. In comparison with the language previously introduced in Lardeux et al (2015) and Lardeux & Monfroy (2014), we can claim that:…”

“…In a previous work (Lardeux et al, 2015), we proposed an efficient system, including a group of encoding rules that could be straightly applied to the CSP set constraint models. Nevertheless, some elements from set definitions could be eliminated without neither losing any solution nor changing the problem semantics.…”

“…In this article, we carry on building on our previous work presented in Lardeux et al (2015) and Lardeux & Monfroy (2014) by proposing our new efficient system with the following new characteristics:…”

From Set Constraint Models to SAT Instances

“…In [13], we presented encoding rules that are directly applied on the CSP models. However, we have noticed that the set variables are not always as small as they could be: some elements could be removed without loosing any solution.…”

“…. Compared to [13], [14], the language as been extended with finite domain variables, and comparison constraints between these variables. Moreover, cardinality is now a constraint linking a finite domain variable to a set variable.…”